模糊值函数的凸性与次可微性

Convexity and sub-differentiability of fuzzy-valued function

在Goetschel-Voxman所定义的序关系下,首先讨论了模糊值函数的凸性,得到了凸模糊值函数的若干充分条件,并证明了凸模糊值函数的Jensen不等式;其次,讨论了凸模糊值函数的次可微性,给出了次微分的若干重要性质,并得到了次可微条件下取得最优解的充分必要条件以及若干个次可微的充分条件.

Under the order relations defined by Goetschel-Voxman. Firstly, we discussed the convexity of fuzzy-valued function,got a number of sufficient conditions about convex fuzzy-valued function, and proved its Jensen inequality. Then,we discussed the sub-differentiability of fuzzy-valued function, and presented many important properties of sub-differential. At the same time, we gained the necessary and sufficient conditions which we obtained the optimum solution under the sub-differential condition and many sufficient conditions of sub-differential.